32dbe23f5e
* fix: clean-up Project Euler 301-320 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
51 lines
1.4 KiB
Markdown
51 lines
1.4 KiB
Markdown
---
|
|
id: 5900f4a31000cf542c50ffb6
|
|
title: 'Problem 311: Biclinic Integral Quadrilaterals'
|
|
challengeType: 5
|
|
forumTopicId: 301967
|
|
dashedName: problem-311-biclinic-integral-quadrilaterals
|
|
---
|
|
|
|
# --description--
|
|
|
|
$ABCD$ is a convex, integer sided quadrilateral with $1 ≤ AB < BC < CD < AD$.
|
|
|
|
$BD$ has integer length. $O$ is the midpoint of $BD$. $AO$ has integer length.
|
|
|
|
We'll call $ABCD$ a biclinic integral quadrilateral if $AO = CO ≤ BO = DO$.
|
|
|
|
For example, the following quadrilateral is a biclinic integral quadrilateral: $AB = 19$, $BC = 29$, $CD = 37$, $AD = 43$, $BD = 48$ and $AO = CO = 23$.
|
|
|
|
<img class="img-responsive center-block" alt="quadrilateral ABCD, with point O, an midpoint of BD" src="https://cdn.freecodecamp.org/curriculum/project-euler/biclinic-integral-quadrilaterals.gif" style="background-color: white; padding: 10px;">
|
|
|
|
Let $B(N)$ be the number of distinct biclinic integral quadrilaterals $ABCD$ that satisfy ${AB}^2 + {BC}^2 + {CD}^2 + {AD}^2 ≤ N$. We can verify that $B(10\\,000) = 49$ and $B(1\\,000\\,000) = 38239$.
|
|
|
|
Find $B(10\\,000\\,000\\,000)$.
|
|
|
|
# --hints--
|
|
|
|
`biclinicIntegralQuadrilaterals()` should return `2466018557`.
|
|
|
|
```js
|
|
assert.strictEqual(biclinicIntegralQuadrilaterals(), 2466018557);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function biclinicIntegralQuadrilaterals() {
|
|
|
|
return true;
|
|
}
|
|
|
|
biclinicIntegralQuadrilaterals();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|